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Find the volume of a right circular cone that has a height of 11.4 in and a
base with a radius of 5.1 in . Round your answer to the nearest tenth of a
cubic inch.
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Ask by Beck Bond. in the United States
Jan 24,2025

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The volume of the cone is approximately 310.5 cubic inches.

Solución

To find the volume of a right circular cone, we can use the formula:
where:
  • is the volume of the cone,
  • is the radius of the base of the cone,
  • is the height of the cone.
Given:
  • Height of the cone, inches,
  • Radius of the base of the cone, inches.
Substitute the given values into the formula:
Now, we can calculate the volume of the cone.
Calculate the value by following steps:
  • step0: Calculate:
  • step1: Convert the expressions:
  • step2: Multiply the terms:
  • step3: Multiply:
  • step4: Evaluate the power:
  • step5: Multiply the fractions:
  • step6: Multiply:

    The volume of the right circular cone is approximately 310.508735 cubic inches.
Rounding to the nearest tenth of a cubic inch, the volume of the cone is approximately 310.5 cubic inches.

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Mind Expander

To calculate the volume of a right circular cone, you can use the formula , where is the radius of the base and is the height. Plugging in the values, we get . This simplifies to roughly , which calculates to about , and finally gives us a volume of approximately cubic inches when rounded to the nearest tenth.
You can visualize a cone as a party hat, and the volume is all about how much cake (or ice cream!) you can fit inside it. This formula is really handy and works for any cone, whether it’s for a birthday celebration or for scientific purposes. Calculators help turn this complex math into a fun game of volume discovery!

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